The Rate of Return for Discounting Non-Life Insurance Loss Reserves

This paper considers the rates of return appropriate for use in the discounting of loss reserves. The author reviews some of the modern theory of term structure of bond interest rates. Discount factors for fixed term single payment future liabilities are developed for the case in which those liabilities are supported by a bond portfolio, and the factors are interpreted within the term structure theory. It is found that the discounted value of the liabilities is equal to the market value of the bond portfolio which provides matching cash flows, provided that such a matching portfolio can be constructed, whether or not such a portfolio is in fact held. The alternative case, in which it cannot be constructed, is also considered. The author considers the financial implications of mismatching between assets and liabilities, when the former comprises only bonds. The mismatch does not affect the value of the liabilities, but does affect the associated risk. This risk may be covered by a provision for adverse deviation (PAD), to be added to the value of liabilities. The PAD is calculated in such a way that the resulting total asset requirement will be sufficient to meet liabilities with prescribed probability. The forward yield curve in existence at the valuation date is central to this evaluation of risk. Also considered is the valuation of liabilities supported by an asset portfolio consisting of only variable return assets, i.e. those other than fixed interest assets. In this case, it is found that liabilities are to be discounted at rates of return essentially equal to the expected (in the statistical sense) rates to be generated by the variable return assets. The CAPM is used to relate these rates to the bond rates implicit in the forward bond yield curve existing at valuation date. The computation of an associated PAD is also discussed. It is suggested throughout the paper that most practical computations need to be carried out by means of simulation. One section relates such simulations to those which have been carried out in recent series of English and Finnish publications respectively.